Problem: Express as a common fraction: $0.\overline5+0.\overline1-0.\overline3$
In general, to express the number $0.\overline{n}$ as a fraction, we call it $x$ and subtract it from $10x$: $$\begin{array}{r r c r@{}l}
&10x &=& n&.nnnnn\ldots \\
- &x &=& 0&.nnnnn\ldots \\
\hline
&9x &=& n &
\end{array}$$ This shows that $0.\overline{n} = \frac{n}{9}$.

Hence, our original problem reduces to computing $\frac 59 + \frac 19 - \frac 39 = \frac 39 = \boxed{\frac 13}$.